Notes
- In order to get full credit in the open ended questions, you need to spend some time reflecting upon and writing your answers. In most of these problems, the probability that a one-sentence answer will get full credit is close to 0 (and so will be what you learn from the exercise)
- Make sure you show all your work on the problems that require it so. Otherwise, even if you give a correct answer, if you do not explain how you obtained it, you'll get very little or no credit.
- It would be great if you discussed ideas with your classmates. The write-up, however, must be done individually.
- Recall that the slides of the lectures can be found here.
Problems
- Write 462 in the traditional Chinese number system,
- Write 55667 in the Mayan number system.
- Is the Greek alphabetic number system positional? Why or why not? (Notes: A yes or no answer, without explanation will get no credit. Here, the definition of positional is the one given in class.)
- Consider the number systems discussed in class
- Egyptian hieroglyphic
- Traditional Chinese
- Mayan
- Cuneiform -or Mesopotamian-
- Greek alphabetic
- Hindu Arabic
- How many numerals does one need to write the number 9987?
- State, if possible, the largest number one can write in this number systems with the numerals listed on the slides. Explain your answer.
- What is the maximum number of times a numeral can appear in a single number? If there is not maximum times a numeral can appear, explain why.
- Explain the difference between a number and a numeral. Give examples, if possible, of
- a number which is not a numeral.
- a numeral which is not a number.
- Why different societies ended up using number systems with different bases, how did their number system reflect how their society used numbers? What benefit comes from using different bases?
- The following is a paragraph from the book "The universal history of numbers", by Georges Ifrah, ``Another example of high numbers it is from a statue from Hieraconpolis, dating from 2800 BCE, where the number of enemies slain by a king called KhaSeKhem is shown as X by the following sign''. You need to find out X, that is the number of enemies slain from the hieroglyphic below. It will come handy to read how the book continues ``Early examples show rather irregular outlines and groupings of the signs.'' given that our example shows such an irregular grouping.
![Hieroglyphic numbers](https://www.math.stonybrook.edu/~moira/courses/mat336-sp2022/images/hierNumber.png)
Hieroglyphic inscription
Sample Quiz 1
- Write 346 in the traditional Chinese number system,
- Write 55667 in the Mesopotamian number system.
- Write in Hindu-Arabic numerals the number given in hieroglyphic above
- Is the Greek alphabetic number system positional? Why or why not? (Notes: A yes or not answer, without explanation will get no credit. Here, the definition of positional is the one given in class.)
Note 1: The numerals in the table below will be given with the quiz.
Note 2: These four questions are chosen to give you an idea of the length of the test. The other problems of the homework are also possible questions (although 4 is a bit too long..)
![numerals](https://www.math.stonybrook.edu/~moira/courses/mat336-sp2023/images/numerals.jpeg)